Rotted sole plate in bathroom

I am doing a remodeling project on a small bathroom. When I removed the old tile and cement board on the floor I noticed part of the subfloor had water damage. I removed the drywall to investigate further and can now see that a section of the sole plate is rotted. This has happened in the area right next to the bathtub where I would guess water has spilled over the edge for years. It may be damaged behind the tub as well but I can not see that area unless I remove the tub. The damaged sole plate has a drainage pipe and water supply for the toilet coming up through it from the crawl space. The wall appears to be a load bearing wall since it had a double header plate.

How would I replace the sole plate? Is it important for the sole plate to be continuous or could it be replaced in sections, making sure to provide support below the vertical studs? Would removing the tub be necessary or a good idea?

Any input is appreciated.

Thanks,

Stan

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Rotted sole plate in bathroom

I encountered the same thing in my bathroom on a load-bearing wall. Yes, the bottom plate needs to be replaced. You do need to temporarily support the wall while you're doing the work. Yes, you can replace it in pieces as opposed to one full length piece.

Here's a couple pictures of how I replaced mine. As you can see, some of my studs were rotten as well, so I cut out and replaced the bad sections and sistered new ones next to them.
You definately need to remove the tub if that's what it takes to get in there and do this right. If the bottom plate is shot, you can rest assured that the plywood is bad too. I even had to replace a chunk of my rim joist beneath the wall.

If you do a couple feet at a time and get good support under the studs, you can probably get away without having to build false supporting walls, but that depends on the house.